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Worst-Case Analysis of an Algorithm for Computing the Greatest Common Divisor of n Inputs

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Coding Theory, Cryptography and Related Areas

Abstract

We give an exact worst-case analysis of an algorithm for computing the greatest common divisor of n inputs. The algorithm is extracted from a 1995 algorithm of de Rooij for fixed-base exponentiation.

Research supported in part by a grant from NSERC.

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References

  1. E. Bach and J. Shallit Algorithmic Number Theory. The MIT Press, 1996.

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  2. T. Cormen, C. Leiserson, and R. Rivest. Introduction to Algorithms. MIT Press, 1989.

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  3. P. de Rooij. Efficient exponentiation using precomputation and vector addition chains In A. de Santis, editor, Advances in Cryptology—EUROCRYPT ’9.4 Proceedings, Vol. 950 of Lecture Notes in Computer Science, pages 389–399. SpringerVerlag, 1995.

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Author information

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Charles Lam

  2. Department of Computer Science, University of Waterloo Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Jeffrey Shallit

  3. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Scott Vanstone

Authors
  1. Charles Lam
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  2. Jeffrey Shallit
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  3. Scott Vanstone
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Editor information

Editors and Affiliations

  1. Fachbereich Informatik, Technische Universität Darmstadt, Alexanderstrasse 10, 64283, Darmstadt, Germany

    Johannes Buchmann

  2. Department of Mathematics, Technical University of Denmark, Bldg. 303, 2800, Lyngby, Denmark

    Tom Høholdt

  3. Fachbereich 6, Mathematik und Informatik, Universität Gesamthochschule Essen, 45117, Essen, Germany

    Henning Stichtenoth

  4. Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-532, C.P. 09340, México, D.F., México

    Horacio Tapia-Recillas

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© 2000 Springer-Verlag Berlin Heidelberg

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Lam, C., Shallit, J., Vanstone, S. (2000). Worst-Case Analysis of an Algorithm for Computing the Greatest Common Divisor of n Inputs. In: Buchmann, J., Høholdt, T., Stichtenoth, H., Tapia-Recillas, H. (eds) Coding Theory, Cryptography and Related Areas. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57189-3_14

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  • DOI: https://doi.org/10.1007/978-3-642-57189-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66248-8

  • Online ISBN: 978-3-642-57189-3

  • eBook Packages: Springer Book Archive

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